They are third cousins, if my counting is correct (they share the same great, great, great grandparents - Victoria and Albert). This was, by no means, uncommon among British Royals. A few examples that predate Elizabeth and Phillip would include:

• George V and Mary Teck (second cousins through George III)
• Edward VII and Alexandra of Denmark (third cousins through Duke Louis of Mecklenburg-Schwerin)
• Victoria and Albert (first cousins through Francis of Saxe-Coburg-Saalfield
• William IV and Adelaide of Saxe-Meiningen (third cousins through Ernest 1 of Saxe-Gotha)
• George IV and his second wife Caroline of Brunswick (first cousins though Frederick, Prince of Wales)
• George III and Charlotte of Mecklenburg-Strelitz (second cousins through Adolf Frederick I of Mecklenburg)
• George II and Caroline of Ansbach (third cousins through John George of Brandenburg)
• George I and Sophia Dorothea of Celle (first cousins through George of Brunswick-Lueneberg)
• Queen Anne and Prince George of Denmark (second cousins through Frederick II of Denmark).

That marks every single reigning monarch of the Royal Family of the United Kingdom with the single exception of Edward VIII, who married the American divorcee Wallis Simpson. There is no known relation between the two.

EDIT: It's worth noting that, from what I understand, cousin marriage beyond the first cousin ranks carries a very minimal risk of genetic defect. Even regular cousin marriage (i.e. first cousins) doesn't carry an especially high risk, just higher than most people would find acceptable. It's also worth noting that cousin marriage is not proscribed in Christianity, which would have been the basis of the moral system of most of these monarchs.

EDIT 2: Thanks for correcting my math, u/purpleistari